Allocating Planning Effort When Actions Expire

Abstract

Making plans that depend on external events can be tricky. For example, an agent considering a partial plan that involves taking a bus must recognize that this partial plan is only viable if completed and selected for execution in time for the agent to arrive at the bus stop. This setting raises the thorny problem of allocating the agent’s planning effort across multiple open search nodes, each of which has an expiration time and an expected completion effort in addition to the usual estimated plan cost. This paper formalizes this metareasoning problem, studies its theoretical properties, and presents several algorithms for solving it. Our theoretical results include a surprising connection to job scheduling, as well as to deliberation scheduling in time-dependent planning. Our empirical results indicate that our algorithms are effective in practice. This work advances our understanding of how heuristic search planners might address realistic problem settings.

Situated Temporal Planning Using Deadline-aware Metareasoning

“…Thus, the planner faces the metareasoning problem of deciding which nodes on the open list to expand in order to maximize the chance of finding a plan before its deadline. Shperberg et al (2019) propose a model of this problem called (AE) 2 ('allocating effort when actions expire') which abstracts away from the planning problem and merely assumes n independent processes. Each process attempts to solve the same problem under time constraints.…”

“…The size of the state-space of the S(AE) 2 MDP is exponential in the number of processes, so it is impractical to fully specify the MDP explicitly or to solve it directly. Furthermore, the S(AE) 2 problem is NP-hard, even for known deadlines (denoted KDS(AE) 2 ) (Shperberg et al 2019).…”

“…However, the reduction was from the Knapsack problem, suggesting the possibility of a pseudo-polynomial time optimal solution algorithm. Shperberg et al (2019) also suggested a greedy, and somewhat ad-hoc, decision rule (denoted hereafter as basic greedy), which worked well in an empirical evaluation with various types of distributions.…”

“…Inspired by the situated planning setting, Shperberg et al (2019) proposed a rational metareasoning (Russell and Wefald 1991) approach for a simplified version of the search problem faced by a situated planner. The problem was simplified in several ways: first, only an abstract version of the metareasoning problem was addressed, and second, distributions over the remaining search time and deadlines were assumed known.…”

Choosing the Initial State for Online Replanning

“…Their main focus lies on finding plans that respect external temporal constraints, such as a deadline for arriving at a bus stop. An associated line of more theoretical work (Shperberg et al 2019;Coles et al 2019) takes as its objective to maximize plan feasibility, leaving aside the notion of overall goal achievement time that we address here. There are also several time-aware heuristic search methods, such as Bugsy (Burns, Ruml, and Do 2013) and Deadline-Aware Search (Dionne, Thayer, and Ruml 2011).…”